As the adoption of electric vehicles accelerates globally, the development of supporting infrastructure, particularly public charging stations, has become a critical focus. In China, the electric vehicle market is expanding rapidly, driven by government policies and consumer demand. However, the uneven distribution and underutilization of public charging stations pose significant challenges. This study addresses these issues by proposing a dual-objective optimization model for site selection, balancing public welfare and economic efficiency. I will explore the key factors influencing site selection, develop a mathematical model, and validate it through numerical analysis and a case study, emphasizing the importance of coverage and cost considerations for China EV infrastructure.
The growth of electric vehicles in China has outpaced the development of charging infrastructure, leading to a mismatch between supply and demand. Public charging stations, as essential service facilities, must be strategically located to maximize accessibility and minimize costs. Existing research often focuses solely on economic factors, neglecting the public service aspect. In this study, I integrate both perspectives to provide a comprehensive approach. The analysis begins with identifying influencing factors using the Analytic Hierarchy Process (AHP), followed by the formulation of a 0-1 integer programming model with dual objectives: maximizing coverage and minimizing total cost. This approach ensures that the network of charging stations serves a broader population while remaining economically viable, which is crucial for the sustainable growth of the China EV ecosystem.
To systematically evaluate the factors affecting site selection, I applied the Analytic Hierarchy Process (AHP). This method helps determine the relative weights of various criteria by structuring them into a hierarchy. The factors are categorized into three main groups: traffic demand, cost factors, and geographical location, with sub-factors under each. Traffic demand reflects the public nature of charging stations, including electricity demand and service radius. Cost factors encompass economic aspects such as construction, operation, user travel, and charging expenses. Geographical location considers both public and economic elements, like traffic convenience and inter-station distance. Through expert evaluations using a 1-9 scale, I constructed judgment matrices and calculated weights, ensuring consistency. The results highlight that geographical location and traffic demand have higher weights, emphasizing coverage, while cost factors are less dominant. This analysis confirms that public charging stations for electric vehicles should prioritize service range over pure cost savings, aligning with the goal of enhancing accessibility for China EV users.
| Criteria Layer | Weight | Sub-Criteria Layer | Weight | Overall Weight |
|---|---|---|---|---|
| Geographical Location | 0.54 | Traffic Convenience | 0.60 | 0.324 |
| Inter-Station Distance | 0.40 | 0.216 | ||
| Traffic Demand | 0.30 | Electricity Demand | 0.56 | 0.168 |
| Service Radius | 0.44 | 0.132 | ||
| Cost Factors | 0.16 | Construction Cost | 0.43 | 0.069 |
| Operation Cost | 0.16 | 0.026 | ||
| User Travel Cost | 0.25 | 0.040 | ||
| Charging Cost | 0.16 | 0.026 |
Based on the AHP results, the overall weight for coverage-related factors (geographical location and traffic demand) is $\omega_1 = 0.84$, while cost-related factors have a weight of $\omega_2 = 0.16$. This indicates that site selection for electric vehicle charging stations should primarily aim to maximize coverage, reflecting public service goals, and secondarily minimize costs, ensuring economic sustainability. These weights guide the dual-objective model formulation, which I will describe in the next section. The emphasis on coverage is particularly relevant for China EV adoption, as it addresses range anxiety and promotes wider usage.
The site selection problem for public charging stations involves choosing optimal locations from candidate sites to serve multiple demand points. I assume a region with $n$ demand points and up to $m$ potential charging station sites ($m < n$). The goal is to maximize service coverage and minimize total cost, considering constraints such as service radius, station capacity, and inter-station distance. The model uses 0-1 decision variables: $X_j = 1$ if a station is built at site $j$, and 0 otherwise; $Y_{ij} = 1$ if demand point $i$ is served by station $j$, and 0 otherwise. The charging demand at point $i$ is split into fast-charging ($q_{ij1}$) and slow-charging ($q_{ij2}$) components, reflecting diverse user needs for electric vehicles.
The first objective is to maximize coverage, weighted by $\omega_1$:
$$ \max Z = \omega_1 \sum_{i=1}^{n} \sum_{j=1}^{m} X_j Y_{ij} (q_{ij1} + q_{ij2}) $$
where $Z$ represents the total service coverage. This objective ensures that more electric vehicle users are served, enhancing public accessibility.
The second objective is to minimize total cost, weighted by $\omega_2$:
$$ \min C = \omega_2 (C_1 + C_2 + C_3 + C_4) $$
Here, $C_1$ is the fixed construction cost, $C_2$ is the operation cost, $C_3$ is the user travel cost, and $C_4$ is the charging cost. The components are defined as follows:
$$ C_1 = \sum_{i=1}^{n} \sum_{j=1}^{m} \frac{r(1+r)^t}{(1+r)^t – 1} \left[ w_i + c_j N_i + (1 + \beta)(q_{ij1} + q_{ij2}) c_d \right] X_j $$
where $r$ is the discount rate, $t$ is the station lifetime, $w_i$ is infrastructure investment, $c_j$ is unit equipment cost, $N_i$ is the number of chargers, $\beta$ is a backup battery coefficient, and $c_d$ is battery cost. This cost is crucial for initial setup of China EV charging networks.
$$ C_2 = \sum_{i=1}^{n} \sum_{j=1}^{m} 365 \left[ \frac{e_1 q_{ij}}{1 – \alpha} + e_2 + e_3 N_i + e_4 (1 + \beta)(q_{ij1} + q_{ij2}) \right] X_j $$
where $e_1$ is charging fee per battery, $e_2$ is daily wage, $e_3$ is maintenance cost per charger, $\alpha$ is grid loss rate, and $e_4$ is battery maintenance coefficient. These operational aspects affect the long-term viability of electric vehicle stations.
$$ C_3 = \sum_{i=1}^{n} \sum_{j=1}^{m} k \eta R_{ij} (q_{ij1} + q_{ij2}) $$
where $k$ is road tortuosity factor, $\eta$ is energy cost per km, and $R_{ij}$ is distance from demand point $i$ to station $j$. This captures user expenses for accessing charging points.
$$ C_4 = \sum_{i=1}^{n} \sum_{j=1}^{m} m \left[ c_t q_{ij} d + \theta (q_{ij1} + q_{ij2}) (c_d + c_g + c_h) \right] X_j $$
where $m$ is working months per year, $c_t$ is battery testing cost, $\theta$ is battery scrap rate, $c_g$ is procurement logistics cost, and $c_h$ is recycling logistics cost. This ensures a holistic view of costs for China EV services.
The model includes several constraints to ensure feasibility and efficiency. The flow constraint ensures that demand is met:
$$ q_{ij} = q_{ij1} + q_{ij2} = q_i Y_{ij} $$
The service radius constraint limits the distance between demand points and stations:
$$ X_j Y_{ij} d_{ij} \leq S $$
where $S$ is the service radius. Station capacity must not be exceeded:
$$ Q_j \geq \sum_{i=1}^{n} X_j (q_{ij1} + q_{ij2}) $$
Each demand point is served by at most one station:
$$ \sum_{j=1}^{m} Y_{ij} \leq 1 $$
And service only occurs if a station is built:
$$ Y_{ij} \leq X_j $$
Inter-station distance is constrained to avoid overlap and ensure coverage:
$$ D_{\text{max}} \geq d_{ij} \geq D_{\text{min}} $$
Finally, the number of stations is limited by resources:
$$ \sum_{j=1}^{m} X_j \leq M $$
These constraints collectively ensure that the site selection for electric vehicle charging stations is practical and effective, addressing both public and economic needs in the China EV context.
To validate the model, I conducted numerical simulations with parameters typical for electric vehicle infrastructure in China. Assume $r = 0.05$, $w_i = 3,000,000$ CNY, $c_j = 500,000$ CNY, $N_i = 40$, $\beta = 0.3$, $c_d = 50,000$ CNY, $e_1 = 50$ CNY, $e_2 = 200$ CNY, $e_3 = 30$ CNY, $e_4 = 20$ CNY, $\alpha = 0.1$, $k = 1.4$, $\eta = 0.2$ CNY/km, $\theta = 0.01$, $m = 12$, $c_t = 500$ CNY/month, $c_g = 500$ CNY, $c_h = 300$ CNY, $S = 4$ km, $D_{\text{min}} = 4$ km. Demand points are randomly generated with coordinates and daily demands, simulating urban areas for China EV usage.
Using Lingo software for solving the 0-1 integer programming model, I computed results for different numbers of charging stations (4 to 7). The solutions were obtained on a computer with an Intel Core i5 processor and 16GB RAM, ensuring efficiency. Two scenarios are compared: one prioritizing maximum coverage and the other minimizing total cost. The outcomes demonstrate the trade-offs between public service and economic efficiency for electric vehicle infrastructure.
| Number of Stations | Coverage Rate (%) | Annual Total Cost (10,000 CNY) | Maximum Service Volume |
|---|---|---|---|
| 4 | 73.33 | 6715.94 | 685 |
| 5 | 80.00 | 7862.42 | 851 |
| 6 | 86.67 | 9008.90 | 963 |
| 7 | 93.33 | 10155.39 | 1138 |
| Number of Stations | Annual Total Cost (10,000 CNY) | Coverage Rate (%) | Maximum Service Volume |
|---|---|---|---|
| 4 | 5733.15 | 41.54 | 632 |
| 5 | 6828.26 | 46.67 | 747 |
| 6 | 8134.77 | 55.70 | 804 |
| 7 | 9243.19 | 62.23 | 859 |
Comparing the two scenarios, the maximum coverage approach yields higher coverage rates and service volumes at the expense of increased cost. For instance, with 4 stations, coverage is 73.33% versus 41.54% in the cost-minimization scenario, while cost increases by 17.14%. As the number of stations grows, the coverage-oriented strategy shows a rising maximum service volume, highlighting its effectiveness for expanding electric vehicle accessibility in China. The trade-off is manageable, as the coverage gain outweighs the cost increase, supporting the dual-objective approach for China EV development.
| Number of Stations | Coverage Increase (%) | Cost Increase (%) | Service Volume Increase (%) |
|---|---|---|---|
| 4 | 76.53 | 17.14 | 8.38 |
| 5 | 71.42 | 15.15 | 13.92 |
| 6 | 55.78 | 10.75 | 19.78 |
| 7 | 49.98 | 9.87 | 32.48 |
In the maximum coverage scenario, station locations are chosen to serve clusters of demand points. For example, with 4 stations, they are placed at points covering multiple demand areas, ensuring broad service. As stations increase to 5, 6, or 7, the layout expands coverage further, demonstrating how strategic placement can enhance the network for electric vehicles. This approach is vital for China EV markets, where urban and suburban disparities exist.
To illustrate real-world application, I consider a case study in a representative urban area of China, similar to districts with charging demand imbalances. Suppose there are 10 demand points with specific coordinates and daily charging needs for electric vehicles. The demands range from 25 to 87 units, reflecting varied usage patterns. Using the model with parameters set for realistic conditions, I determine the optimal sites for 4 charging stations. The selected locations maximize coverage, serving multiple demand points and achieving an 80% coverage rate with a service volume of 487. This outcome shows how the model can address actual challenges in China EV infrastructure, such as concentrated demand in central areas and neglected peripherals.
The case study confirms that the dual-objective model effectively balances public service and economic factors. By prioritizing coverage, the solution ensures that more electric vehicle users have access to charging, reducing range anxiety and promoting adoption. The cost increase is justified by the significant improvement in service, which is essential for the growth of the China EV industry. This practical implementation underscores the model’s utility in guiding policy and investment decisions.
In conclusion, this study addresses the critical issue of public charging station site selection for electric vehicles in China by integrating public welfare and economic efficiency. The AHP analysis reveals that coverage-related factors, such as geographical location and traffic demand, are paramount, while cost factors are secondary. The dual-objective 0-1 programming model successfully maximizes coverage and minimizes cost, with numerical results showing that coverage-oriented strategies yield substantial benefits in service volume with acceptable cost increments. As the electric vehicle market evolves, this approach provides a robust framework for optimizing infrastructure development. Future research could incorporate dynamic factors like varying battery types, charging speeds, and time-dependent demand to further refine site selection for China EV charging networks.
The expansion of electric vehicles in China necessitates a coordinated effort to build efficient and accessible charging infrastructure. By applying the proposed model, stakeholders can make informed decisions that enhance public service while maintaining economic viability. This contributes to sustainable transportation and supports national goals for electric vehicle adoption, ultimately fostering a greener and more connected urban environment for all.